Electrical Properties Tomography: A Methodological Review

Abstract

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

EPTlib: An Open-Source Extensible Collection of Electric Properties Tomography Techniques

“…On the one hand, this allowed us to obtain almost identical reconstructions as those reported in Figure 6 if the phase-based approximated Helmholtz-EPT technique was adopted instead of the complete one. On the other hand, the estimation of the relative permittivity ε r was significantly affected by the Laplacian of the Tx sensitivity (7), whose small variations were easily suppressed by the noise. As a consequence, the distributions of ε r recovered by applying Helmholtz-EPT with the adopted filter windows on the noisy input data were extremely noisy and completely unreadable.…”

“…Electric properties tomography (EPT) is a MRI-based quantitative imaging technique which reconstructs the distribution of the electric properties (EPs), conductivity σ and relative permittivity ε r , of the biological tissues at the Larmor frequency of the used MRI scanner [4][5][6][7]. The benefit of a reliable EPT is twofold: on the one hand, EPT can be used as a diagnostic tool, since the electric conductivity of the biological tissues acts as a physical biomarker for some pathologies [8,9]; on the other hand, the knowledge of the actual distribution of the EPs would allow planning electromagnetic-based therapies, like oncological hyperthermia, specifically for each patient [10,11].…”

“…The benefit of a reliable EPT is twofold: on the one hand, EPT can be used as a diagnostic tool, since the electric conductivity of the biological tissues acts as a physical biomarker for some pathologies [8,9]; on the other hand, the knowledge of the actual distribution of the EPs would allow planning electromagnetic-based therapies, like oncological hyperthermia, specifically for each patient [10,11]. A plethora of different techniques implementing EPT has been proposed in the literature [7]. Despite there exist some peculiar approaches to EPT, like the one based on the water content estimated by T 1 -weighted images [12][13][14], almost all the proposed techniques map the EPs by elaborating the distribution of the rotating component B + 1 of the radiofrequency magnetic field B 1 generated by the MRI scanner [7].…”

“…A plethora of different techniques implementing EPT has been proposed in the literature [7]. Despite there exist some peculiar approaches to EPT, like the one based on the water content estimated by T 1 -weighted images [12][13][14], almost all the proposed techniques map the EPs by elaborating the distribution of the rotating component B + 1 of the radiofrequency magnetic field B 1 generated by the MRI scanner [7]. The magnitude |B + 1 |, namely the transmit (Tx) sensitivity, and the phase ϕ + , namely the Tx phase, of B + 1 are usually acquired separately.…”

Effects of Simulated Error-Sources on Different 3-D CSI-EPT Strategies

“…The retrieval of EPs of biological tissue from measurements of magnetic fields generated by radiofrequency coils in a magnetic resonance imaging (MRI) scanner is called electrical properties tomography (EPT) and is a topic that has gained increasing attention in the last few years (see, for example, the three recent reviews [3], [5], [6]). Most EPT methods are based on a modified Helmholtz equation derived from Maxwell's equations in differential form, which shows the direct relationship between the EPs and the magnetic field strength (H), given by…”